Department of Aeronautical and Aviation Engineering
Due Date: 13 March 2025
This assignment focuses on processing GNSS Software-Defined Receiver (SDR) signals to develop a deeper understanding of GNSS signal processing. Students will analyze two real Intermediate Frequency (IF) datasets collected in different environments: open-sky and urban. The urban dataset contains multipath and non-line-of-sight (NLOS) effects, which can degrade positioning accuracy.
| Environment | Carrier Frequency | IF Frequency | Sampling Frequency | Data Format | Ground Truth Coordinates | Data Length | Collection Date (UTC) |
|---|---|---|---|---|---|---|---|
| Open-Sky | 1575.42 MHz | 4.58 MHz | 58 MHz | 8-bit I/Q samples | (22.328444770087565, 114.1713630049711) | 90 seconds | 14/10/2021 12.21pm |
| Urban | 1575.42 MHz | 0 MHz | 26 MHz | 8-bit I/Q samples | (22.3198722, 114.209101777778) | 90 seconds | 07/06/2019 04.49am |
Figure 0. Data Collection Locations
Process the IF data using a GNSS SDR and generate the initial acquisition results.
Solution:
Figure 1.1 Not Acquired Signal
Figure 1.2 Acquired Signal
Figure 1.3 Open-Sky Acquisition Results
Figure 1.4 Urban Acquisition Results
Adapt the tracking loop (DLL) to generate correlation plots and analyze the tracking performance. Discuss the impact of urban interference on the correlation peaks. (Multiple correlators must be implemented for plotting the correlation function.)
Solution:
Figure 2.1 Tracking Results for Open-Sky PRN 16
Figure 2.2 Open-Sky Correlation Results with Multi-correlator in 4 Epochs
Figure 2.3 Urban Correlation Results with Multi-correlator in 4 Epochs
Figure 2.4 Tracking Results for Urban PRN 1
Discussion
| Channel | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Mean CNo in open sky | 36.961 | 36.770 | 36.288 | 35.288 | 36.090 |
| Mean CNo in urban | 52.658 | 46.190 | 38.830 | 37.574 | / |
Impact of Urban Interference
- Higher CNo in urban: Although reflected signals can cause both constructive and destructive interference, the results show higher CNo values in urban environments. This may be due to factors such as antenna gain or other influences that need to be evaluated in future research.
- Pseudorange bias: Signals arriving via NLOS (Non-Line-of-Sight) paths introduce biases in the pseudorange measurements, affecting the accuracy of positioning.
- Difficulty in finding peak: In open sky environments, the DLL (Delay Lock Loop) performs well with clear correlation peaks, enabling accurate tracking. However, in urban environments, the DLL performance degrades due to interference, resulting in broader correlation peaks and making accurate tracking more challenging.
Decode the navigation message and extract key parameters, such as ephemeris data, for at least one satellite.
Solution:
| Parameters | Description | Value |
|---|---|---|
| PRN | Pseudo-Random Noise code number identifying individual satellites | 16, 22, 26, 27, 31 |
| C_ic | Cosine correction term for orbit inclination, correcting periodic orbit inclination changes | -1.01E-07, -1.01E-07, -2.05E-08, 1.08E-07, -1.14E-07 |
| omega_0 | Longitude of ascending node, longitude where satellite orbit crosses Earth | -1.67426, 1.272735, -1.81293, -0.71747, -2.78727 |
| C_is | Sine correction term for orbit inclination, correcting periodic orbit inclination changes | 1.36E-07, -9.31E-08, 8.94E-08, 1.15E-07, -5.03E-08 |
| i_0 | Orbit inclination, angle between satellite | 0.971603, 0.936455, 0.939912, 0.974728, 0.955883 |
| C_rc | Cosine correction term for semi-major axis, correcting periodic semi-major axis changes | 237.6875, 266.3438, 234.1875, 230.3438, 240.1563 |
| omega | Argument of perigee, angle between ascending node and perigee in satellite orbit | 0.679609, -0.88789, 0.295685, 0.630882, 0.311626 |
| omegaDot | Rate of change of right ascension of ascending node | -8.01E-09, -8.67E-09, -8.31E-09, -8.02E-09, -7.99E-09 |
| IODE_sf3 | Ephemeris data version identifier | 9, 22, 113, 30, 83 |
| iDot | Rate of change of orbit inclination | -4.89E-10, -3.04E-11, -4.18E-10, -7.14E-13, 3.21E-11 |
| idValid | Validity of satellite signal identifiers | [2,0,3], [2,0,3], [2,0,3], [2,0,3], [2,0,3] |
| weekNumber | Week number of satellite launch, determining data timeliness | 1155, 1155, 1155, 1155, 1155 |
| accuracy | Accuracy of satellite data | 0, 0, 0, 0, 0 |
| health | Satellite health status | 0, 0, 0, 0, 0 |
| T_GD | GPS signal group delay difference | -1.02E-08, -1.77E-08, 6.98E-09, 1.86E-09, -1.30E-08 |
| IODC | Ephemeris data identifier for detecting changes | 234, 218, 15, 4, 228 |
| t_oc | Ephemeris reference time | 396000, 396000, 396000, 396000, 396000 |
| a_f2 | Second-order term coefficient for satellite clock correction | 0, 0, 0, 0, 0 |
| a_f1 | First-order term coefficient for satellite clock correction | -6.37E-12, 9.21E-12, 3.98E-12, -5.00E-12, -1.93E-12 |
| a_f0 | Zero-order term coefficient for satellite clock correction | -0.00041, -0.00049, 0.000145, -0.00021, -0.00014 |
| IODE_sf2 | Ephemeris data version identifier (Part 2) | 9, 22, 113, 30, 83 |
| C_rs | Sine correction term for semi-major axis | 23.34375, -99.8125, 21.25, 70.4375, 30.71875 |
| deltan | Mean motion difference | 4.25E-09, 5.28E-09, 5.05E-09, 4.03E-09, 4.81E-09 |
| M_0 | Mean anomaly at reference time | 0.718117, -1.26097, 1.735571, -0.17302, 2.824523 |
| C_uc | Cosine correction term for orbital eccentricity | 1.39E-06, -5.16E-06, 1.15E-06, 3.73E-06, 1.46E-06 |
| e | Orbital eccentricity | 0.012296, 0.006714, 0.006254, 0.009574, 0.010272 |
| C_us | Sine correction term for orbital eccentricity | 7.69E-06, 5.17E-06, 7.04E-06, 8.24E-06, 7.23E-06 |
| sqrtA | Square root of semi-major axis | 5153.771, 5153.712, 5153.636, 5153.652, 5153.622 |
| t_oe | Ephemeris reference time | 396000, 396000, 396000, 396000, 396000 |
| TOW | Time of Week | 390102, 390102, 390102, 390102, 390102 |
Using the pseudorange measurements obtained from tracking, implement the Weighted Least Squares (WLS) algorithm to compute the user's position and velocity.
- Plot the user position and velocity.
- Compare the results with the ground truth. (Please see Task 5)
- Discuss the impact of multipath effects on the WLS solution.
Solution:
Weighted Least Squares (WLS) Algorithm:
The WLS algorithm is used to estimate the user's position and velocity based on pseudorange measurements. The algorithm minimizes the weighted sum of squared residuals between the measured pseudoranges and the pseudoranges calculated based on the estimated position.
The cost function for WLS is given by:
Where:
-
$\mathbf{x}$ is the state vector (position and velocity). -
$\mathbf{y}$ is the vector of pseudorange measurements. -
$\mathbf{H}$ is the design matrix that maps the state vector to the measurements. -
$\mathbf{W}$ is the weight matrix. In the WLS position solving,$\mathbf{W}$ is a diagonal matrix with diagonal elements being sin(el). And in the velocity solving, W is set as the identity matrix$I$ (According to RTKLIB 1)
The solution is obtained by solving:
- The user position in opensky and urban scenario are displayed below.
Figure 4.1 WLS Position Results for Open-Sky
Figure 4.2 WLS Position Results for Urban
Discussion
- Both position and velocity errors are greater in urban scenarios than in open-sky ones. This is mainly attributed to the pseudorange and Doppler frequency measurement errors caused by multipath effects and non-line-of-sight (NLOS) propagation, which make accurate location determination more challenging.
- In urban settings, the Doppler frequency for channel 2 may exceed 4.0e3, which is much higher than that of the other channels. This discrepancy prevents the WLS receiver velocity from converging and introduces significant errors. However, as there are only four acquired satellites, I cannot perform fault detection and exclusion.
Develop an Extended Kalman Filter (EKF) using pseudorange and Doppler measurements to estimate user position and velocity.
Solution: Extended Kalman Filter (EKF):
The EKF is a recursive algorithm used to estimate the state of a nonlinear system. The algorithm linearizes the system model around the current state estimate using a Taylor series expansion and then applies the Kalman filter equations.
The EKF algorithm consists of two main steps: prediction and update.
Prediction Step:
Where:
-
$\mathbf{x}_{k|k-1}$ is the predicted state estimate. -
$\mathbf{P}_{k|k-1}$ is the predicted error covariance. -
$f$ is the state transition function. -
$\mathbf{F}_k$ is the Jacobian matrix of$f$ evaluated at$\mathbf{x}_{k-1|k-1}$ . -
$\mathbf{Q}_k$ is the process noise covariance matrix.
Update Step:
Where:
-
$\mathbf{y}_k$ is the measurement residual. -
$\mathbf{S}_k$ is the measurement covariance. -
$h$ is the measurement function. -
$\mathbf{H}_k$ is the Jacobian matrix of$h$ evaluated at$\mathbf{x}_{k|k-1}$ . -
$\mathbf{R}_k$ is the measurement noise covariance matrix. -
$\mathbf{K}_k$ is the Kalman gain. -
$\mathbf{x}_{k|k}$ is the updated state estimate. -
$\mathbf{P}_{k|k}$ is the updated error covariance.
Figure 5.1 Open-Sky Position Solution with WLS and EKF
Figure 5.2 Open-Sky Velocity Solution with WLS and EKF
Figure 5.3 Urban Position Solution with WLS and EKF
Figure 5.4 Urban Velocity Solution with WLS and EKF
Discution:
- The results show that the WLS position solution may outperform the EKF solution. This is attributed to the errors in the Doppler frequency, which impact the predicted state and subsequently introduce inaccuracies in the solutions.
- However, the velocity results obtained from the EKF are superior to those from WLS. The EKF, with its recursive update mechanism and noise suppression capability, is generally more effective in handling errors and maintaining relatively stable estimation results.
Thanks for kimichat polishing the format.
- Takasu Tomoji. (2009). RTKLIB: Open Source Program Package for RTK-GPS. FOSS4G 2009. Tokyo, Japan, November 2, 2009.
- SoftGNSS (https://github.com/TMBOC/SoftGNSS)